Condensate clouds fundamentally impact the atmospheric structure and spectra of exoplanets and brown dwarfs but the connections between surface gravity , cloud structure , dust in the upper atmosphere , and the red colors of some brown dwarfs remain poorly understood . Rotational modulations enable the study of different clouds in the same atmosphere , thereby providing a method to isolate the effects of clouds . Here we present the discovery of high peak-to-peak amplitude ( 8 % ) rotational modulations in a low-gravity , extremely red ( J- K _ { s } =2.55 ) L6 dwarf WISEP J004701.06+680352.1 ( W0047 ) . Using the Hubble Space Telescope ( HST ) time-resolved grism spectroscopy we find a best-fit rotational period ( 13.20 \pm 0.14 hours ) with a larger amplitude at 1.1 micron than at 1.7 micron . This is the third largest near-infrared variability amplitude measured in a brown dwarf , demonstrating that large-amplitude variations are not limited to the L/T transition but are present in some extremely red L-type dwarfs . We report a tentative trend between the wavelength dependence of relative amplitude , possibly proxy for small dust grains lofted in the upper atmosphere , and the likelihood of large-amplitude variability . By assuming forsterite as haze particle , we successfully explain the wavelength dependent amplitude with submicron-sized haze particles sizes of around 0.4 \mu m . W0047 links the earlier spectral and later spectral type brown dwarfs in which rotational modulations have been observed ; the large amplitude variations in this object make this a benchmark brown dwarf for the study of cloud properties close to the L/T transition .